MOSCOW - Vladimir Putin's daring bid to host the Winter Olympics in the politically dicey Caucasus Mountains was his way of showing to the world that he had created a stylish, fun-loving country, a Russia that had defeated violent separatism once and for all.

It was a gutsy gamble - and the remaining separatists vowed to do whatever they could to disrupt the pageant. The potential costs of failure were driven home Monday when an apparent suicide bomber shredded a crowded trolley bus in the city of Volgograd. That came on the heels of a bomb attack on the city's railroad station the day before. The two explosions killed 31 people and injured dozens more.

Security at the site of the Olympics is watertight, so Islamist extremists have vowed to bring violence to the Russian heartland. Volgograd, only about 400 miles from Sochi, and a city storied in Russian history, offers itself as a tempting target.

Putin demanded a tightening of security Monday amid fears that foreign guests in particular could be frightened away from the Winter Games. The two bomb blasts effectively blunt his recent charm offensive, seemingly aimed at the West with the Olympics in mind, that saw the release of the oil tycoon Mikhail Khodorkovsky, two of the Pussy Riot members and the crew of the Greenpeace ship Arctic Sunrise, held on criminal charges since late summer.

Although no groups claimed responsibility for the Volgograd attacks, officials said they believe they were related - and linked to an extremist group in Dagestan.

Russia has been engaged in an enduring and violent struggle with extremists ever since it defeated a separatist movement in Chechnya in the 1990s. After the war ended, a growing number of separatists turned radical, evolving into Islamist extremists who have launched sporadic terrorist attacks on the country, from Moscow to the hinterlands.

Putin has staked his prestige on hosting a successful winter Games in Sochi, and demonstrating in the process the safety of the resorts at the western end of the Caucasus mountain range.

The security agencies have been clamping down hard in Sochi, watching and calling in for questioning those who express unwelcome opinions, including environmental and human rights activists. Russia is spending $2 billion on security there.

IOC President Thomas Bach is fully confident Russian authorities will deliver a "safe and secure" Olympics in Sochi despite the two deadly suicide bombings in southern Russia that heightened concerns about the terrorist threat to the Games, the Associated Press reported.

The heavy protection for Sochi appears to have drawn resources away from security operations in other parts of this huge country. On Monday, Putin met with the head of Russia's Federal Security Service and directed him to prepare plans for heightened security nationwide.

The National Anti-Terrorist Committee announced Monday that more than 4,000 security personnel will be involved in a huge security sweep in Volgograd. Volunteers were also being organized to patrol the sprawling city along the Volga River, where Soviet and Nazi forces met in an epic World War II battle in 1942 and 1943, when the city was known as Stalingrad.

The chance that terrorist activity will spoil the Olympics has been a prime worry for security officials.

Doku Umarov, a Chechen rebel leader who authorities think is operating out of Dagestan and leading a movement to establish an Islamic emirate in southern Russia, called in July for resuming a campaign of terrorist attacks against civilian targets in Russia. He denounced the Sochi Games as a defilement of the sacred ground of the area's original inhabitants, the Circassians.

Umarov has taken responsibility for several terror attacks, including a bombing at a Moscow's Domodedovo airport in January 2011 that killed 37 people. The United States has offered a reward of up to $5 million for information about Umarov, U.S. Ambassador Michael McFaul said on Twitter on Monday.

In a statement released by the White House, the spokeswoman for the National Security Council, Caitlin Hayden, said, "The U.S. government has offered our full support to the Russian government in security preparations for the Sochi Olympic Games, and we would welcome the opportunity for closer cooperation for the safety" of athletes and others.

Sunday's bombing took place, according to officials, when a railroad inspector at a station entrance tried to stop a man who looked suspicious.

The attack on the trolley bus Monday also appears to have been the work of a suicide bomber, officials said. The roof was blown off the bus, shattering windows in a building nearby. Investigators calculated that the bomber was carrying about nine pounds of explosives. Fourteen people are confirmed dead.

The bombings wounded 104, according to Russia's Health Ministry. As of late Monday, 58 remained hospitalized, many in grave condition, the AP reported.